Veteran Families Fairness Act - Provides for the payment of certain accrued veterans' benefits to the estate of a deceased veteran upon the veteran's death if the veteran has no living spouse, children, or dependent parents.

Allows the estate of a veteran who dies while his or her claim for accrued veterans' benefits is pending to file a request to be substituted as the claimant.

Requires the Secretary of Veterans Affairs (VA) to process the claim of a substituted claimant: (1) by recognizing the original filing date of the claim, and (2) without penalty to the priority of the claim.

Directs the Secretary to notify the estates of veterans who died before this Act's enactment of their eligibility to apply for the deceased veteran's accrued benefits or apply to act as a substituted claimant. Gives estates one year after the date they received such notification to make such an application.

Requires the Secretary to reimburse a successful veterans' benefits claimant for the medical costs that: (1) were charged to the claimant while the claim was pending, and (2) would have been reimbursed or provided by the VA if the treatment occurred after the claim was approved. Directs the Secretary to recommend to each claimant, when they file a claim, to retain documentation regarding such costs.